
Here \(\beta \equiv \tilde{k}r_{c}/\mu _{n}\) , \(z\equiv (\mu _n/\tilde{k} r_c) e^{\tilde{k} r_c \varphi }\) , \(G_{i,j}^{k,l}\)  are Meijer-G functions [1]} , \(_i F_j\)  are Hypergeometric functions. \(c_1\)  is a normalization constant given in Eq. REF  and \(c_3\)  and \(c_4\)  are constants that are determined from the Neummann boundary condition that the wavefunction must satisfy. Additionally, we provide these expressions as well as those valid also for arbitrary values of \(\tilde{k}r_c\)  in supplementary Mathematica files on GitHub.
